Consider a simple example of moral hazard. suppose that woodrow goes into a casino to make one bet a day. the casino is very basic; it has two bets: a safe bet and a risky bet. in the safe bet, a nickel is flipped. if the nickel lands on heads, woodrow wins $ 100 . if it lands on tails, woodrow loses $ 100 . the risky bet is similar: a silver dollar is flipped. if the silver dollar lands on heads, woodrow wins $ 5,000 . if it lands on tails, woodrow loses $ 10,000 . each coin has a 50 % chance of landing on each side. what is the expected value of the safe bet?

The expected value of the safe bet equal $0

Step-by-step explanation:

If  

is a finite numeric sample space and

for k=1, 2,..., n

is its probability distribution, then the expected value of the distribution is defined as

What is the expected value of the safe bet?

In the safe bet we have only two possible outcomes: head or tail. Woodrow wins $100 with head and “wins” $-100 with tail So the sample space of incomes in one bet is

S = {100,-100}

Since the coin is supposed to be fair,  

P(X=100)=0.5

P(X=-100)=0.5

and the expected value is

E(X) = 100*0.5 - 100*0.5 = 0

its a straight line parallel to the time axis

its line 2 i just added the rest or else it wouldn't let me answer